A couple things to try in order to troubleshoot. These aren't permanent solutions, just ways to try to isolate the problem and give Zimbra what they need to fix it, if they can.
First, create a separate account on your Mac and set up a CalDAV connection from scratch to your account. Reason for doing this is that
based on my experience, iCal leaves some stuff sitting around even when you delete/recreate an existing connection.
Second, try using Thunderbird (current is 2.0.0.23) with Lightning 0.9.
In Lightning you set up access to Calendars one-by-one (even if you have multiple calendars or they're shared to you). E.g. for my main calendar the location is
https://serverName/dav/myUserName/Calendar and for someone else's it's
https://servername/dav/theirUserName/Calendar.